Question: Simplify the following expression: $ x = \dfrac{-4t + 5}{-7t + 4} + \dfrac{4}{3} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{3}{3}$ $ \dfrac{-4t + 5}{-7t + 4} \times \dfrac{3}{3} = \dfrac{-12t + 15}{-21t + 12} $ Multiply the second expression by $\dfrac{-7t + 4}{-7t + 4}$ $ \dfrac{4}{3} \times \dfrac{-7t + 4}{-7t + 4} = \dfrac{-28t + 16}{-21t + 12} $ Therefore $ x = \dfrac{-12t + 15}{-21t + 12} + \dfrac{-28t + 16}{-21t + 12} $ Now the expressions have the same denominator we can simply add the numerators: $x = \dfrac{-12t + 15 - 28t + 16}{-21t + 12} $ $x = \dfrac{-40t + 31}{-21t + 12}$ Simplify the expression by dividing the numerator and denominator by -1: $x = \dfrac{40t - 31}{21t - 12}$